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1. Role of Phosphorus Type and Biodegradable Polymer on Phosphorus Fate and Efficacy in a Plant–Soil System

   https://doi.org/10.1021/acs.jafc.3c04735  

   Sigmon, Leslie R.; Vaidya, Shital R.; Thrasher, Corey; Mahad, Sumaya; Dimkpa, Christian O.; Elmer, Wade; White, Jason C.; Fairbrother, D. Howard (November 2023, Journal of Agricultural and Food Chemistry)

   Phosphorus (P) is critical for crop production but has a high nutrient use inefficiency. Tomato was grown in soil amended with five P-sources, used as-is, or embedded within a biodegradable polymer, polyhydroxyalkanoate (PHA). Correlation analysis identified treatments that maintain plant growth, improve bioavailable soil P, and reduce P loss. Three performance classes were identified: (i) micro- and nanohydroxyapatite, which did not increase bioavailable P, plant P-uptake, or change P in runoff/leaching compared to controls; (ii) monocalcium phosphate (MCP), dicalcium phosphate (DCP), calcium pyrophosphate nanoparticles (CAP), and PHA-MCP that increased P-uptake and/or bioavailable P but also increased P loss in runoff/leaching; and (iii) PHA-DCP and PHA-CAP, where increased bioavailable P and plant P-uptake were achieved with minimal P loss in runoff/leaching. In addition to identifying treatments that maintain plant growth, increase bioavailable P, and minimize nutrient loss, correlation plots also revealed that (i) bioavailable P was a good indicator of plant P-uptake; (ii) leached P could be predicted from water solubility; and (iii) P loss through runoff versus leaching showed similar trends. This study highlights that biopolymers can promote plant P-uptake and improve bioavailable soil P, with implications for mitigating the negative environmental impacts of P loss from agricultural systems. 

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2. Limit models in strictly stable abstract elementary classes

   https://doi.org/10.1002/malq.202200075  

   Boney, Will; VanDieren, Monica_M (December 2024, Mathematical Logic Quarterly)

   Abstract In this paper, we examine the locality condition for non‐splitting and determine the level of uniqueness of limit models that can be recovered in some stable, but not superstable, abstract elementary classes. In particular we prove the following. Suppose that is an abstract elementary class satisfyingthe joint embedding and amalgamation properties with no maximal model of cardinality ,stability in ,,continuity for (i.e., if and is a limit model witnessed by for some limit ordinal and there exists so that does not ‐split over for all , then does not ‐split over ). Then for and limit ordinals both with cofinality , if satisfies symmetry for (or just ‐symmetry), then, for any and that are and ‐limit models over , respectively, we have that and are isomorphic over . Note that no tameness is assumed. 

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3. Counting points on smooth plane quartics

   https://doi.org/10.1007/s40993-022-00397-8  

   Costa, Edgar; Harvey, David; Sutherland, Andrew V. (March 2023, Research in Number Theory)

   Abstract We present efficient algorithms for counting points on a smooth plane quartic curve X modulo a prime p . We address both the case where X is defined over  $${\mathbb {F}}_p$$ F p and the case where X is defined over $${\mathbb {Q}}$$ Q and p is a prime of good reduction. We consider two approaches for computing $$\#X({\mathbb {F}}_p)$$ # X ( F p ) , one which runs in $$O(p\log p\log \log p)$$ O ( p log p log log p ) time using $$O(\log p)$$ O ( log p ) space and one which runs in $$O(p^{1/2}\log ^2p)$$ O ( p 1 / 2 log 2 p ) time using $$O(p^{1/2}\log p)$$ O ( p 1 / 2 log p ) space. Both approaches yield algorithms that are faster in practice than existing methods. We also present average polynomial-time algorithms for $$X/{\mathbb {Q}}$$ X / Q that compute $$\#X({\mathbb {F}}_p)$$ # X ( F p ) for good primes $$p\leqslant N$$ p ⩽ N in $$O(N\log ^3 N)$$ O ( N log 3 N ) time using O ( N ) space. These are the first practical implementations of average polynomial-time algorithms for curves that are not cyclic covers of $${\mathbb {P}}^1$$ P 1 , which in combination with previous results addresses all curves of genus $$g\leqslant 3$$ g ⩽ 3 . Our algorithms also compute Cartier–Manin/Hasse–Witt matrices that may be of independent interest. 

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4. Natural selection favours a larger eye in response to increased competition in natural populations of a vertebrate

   https://doi.org/10.1111/1365-2435.13334  

   Beston, Shannon M.; Walsh, Matthew R.; Higham, ed., Timothy (April 2019, Functional Ecology)

   Abstract Eye size varies notably across taxa. Much work suggests that this variation is driven by contrasting ecological selective pressures. However, evaluations of the relationship between ecological factors and shifts in eye size have largely occurred at the macroevolutionary scale. Experimental tests in nature are conspicuously absent.Trinidadian killifish,Rivulus hartii, are found across fish communities that differ in predation intensity. We recently showed that increased predation is associated with the evolution of a smaller eye. Here, we test how divergent predatory regimes alter the trajectory of eye size evolution using comparative mark–recapture experiments in multiple streams.We found that increases in eye size are associated with enhanced survival, irrespective of predation intensity. More importantly, eye size is associated with enhanced growth in communities that lack predators, while this trend is absent when predators are present.Such results argue that increased competition for food in sites that lack predators is the key driver of eye size evolution. Aplain language summaryis available for this article. 

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5. Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian

   https://doi.org/10.1090/tran/8903  

   Bañuelos, Rodrigo; Mariano, Phanuel; Wang, Jing (August 2023, Transactions of the American Mathematical Society)

   For domains in R d \mathbb {R}^d , d ≥ 2 d\geq 2 , we prove universal upper and lower bounds on the product of the bottom of the spectrum for the Laplacian to the power p > 0 p>0 and the supremum over all starting points of the p p -moments of the exit time of Brownian motion. It is shown that the lower bound is sharp for integer values of p p and that for p ≥ 1 p \geq 1 , the upper bound is asymptotically sharp as d → ∞ d\to \infty . For all p > 0 p>0 , we prove the existence of an extremal domain among the class of domains that are convex and symmetric with respect to all coordinate axes. For this class of domains we conjecture that the cube is extremal. 

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